The SP equation (REF ) was proposed to describe the propagation of ultra-short optical pulses in silica optical fibers [1]}. Pulse propagation in optical fibers is usually modeled by the cubic nonlinear Schr\(\ddot{o}\) dinger (NLS) equation [2]}. So NLS equation forms the basis for optimizing existing fiber links and suggesting new fiber communication systems in attempts to achieve high bit-rate data transmission. However, it is questionable that the validity of the NLS equation as a slowly varying amplitude approximation of Maxwell's equations can describe the propagation of these very narrow pulseless. But the SP equation describes the evolution of a short pulse in nonlinear media if the pulse center is far from the nearest resonance frequency of the material's susceptibility. In some sense it represents the opposite extreme from the NLS approximation since that results from expanding the susceptibility in the frequency while equation results from expanding the susceptibility in the wavelength, which means the SP equation provides an increasingly better approximation to the corresponding solution of the Maxwell equations as the pulse duration shortens [3]}. However, we can find that the SP equation appeared first as one of Rabelo's equations which describe photospherical surfaces, possessing a zero-curvature representation [4]}.
